Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

KIr ---> 00.

(11.12)

space, but the

(11.10)

(11.11)

imperfect capital mobility.

at the commercial banks plu, powered money:

(11.80

open economy

unexciting (but rather essen-

.,a1 content by specifying

1.2) in the form of a condition t as:

(11.9)

. _-pends on the rate of interest venous level of government

as a function of output and e E is the nominal exchange 1)s is the foreign price level, lition of the exchange rate, a s represented by an increase

I

Brest rate and the marginal n zero and unity, we have

port function satisfies Xy < 0 > 0 (as it is assumed that he open economy IS curve.

(-Ting in (r, Y) :omy. fashion.

1 11.10)411.11) define the ( r, Y) space. The modifica- the economy consists of

ra fraction ci of their deposits as hermore that the public desires

= c-2. Then, since Ms D + CP = 1 --c2)/(ci +c2 ) > 1. A higher legal

lecrease the money multiplier.

Chapter 11: The Open Economy

.rie potential endogeneity of the money supply through changes in the stock of 'et foreign assets of the central bank. The model is closed by assuming that both )mestic and foreign prices are fixed (and normalized to unity, i.e. P* = P = 1), and by making an assumption regarding the degree of international capital mobility.

11.1.3 Capital mobility and economic policy

We can distinguish several degrees of "financial openness" of an economy. First, it can be assumed that the small open economy (SOE) has no trade in financial assets with the rest of the world (ROW). This extreme case is referred to as one of capital immobility. This case was relevant during the 1940s and early 1950s when many countries had capital controls. A second case is that of perfect capital mobility. Financial capital is perfectly mobile and flows to that location where it earns the highest yield. Domestic and foreign bonds are perfect substitutes and portfolio adjustment is instantaneous so that yields are equated across the world. This case is often deemed to be relevant to the situation in the 1980s and 1990s. Finally, the intermediate case

is referred to as one of

The balance of payments B can be written as the sum of the current account and the capital account. Ignoring net international transfers the former coincides with

the trade account:

B X(Y, Q) KI(r — r*) ANFA cb , (11.13)

where B is the balance of payments, KI is net capital inflows, and r* is the interest rate in the ROW. If KI is positive this means that domestic residents are selling

more financial assets (such as bonds) to the ROW than they are buying from the ROW. In that case the country as a whole is a net borrower from the ROW. The three assumptions regarding capital mobility that were mentioned above can now be made more precise. Capital immobility (case (i)) means that KI(r — r*) 17. 0 so that balance of payments equilibrium coincides with equilibrium on the current account, i.e. B = ANFAcb = X(Y, Q) = 0. With perfect capital mobility (case (ii)), arbitrage in the capital markets and the resulting capital flows ensure that r = r* always, which can be represented mathematically by Finally, for the case of imperfect capital mobility (case (iii)) differences between r and r* can exist in equilibrium and 0 < KIr << 00. Figure 11.1 shows the balance of payments (BP) curves in (r, Y) space for the different cases. The slope of the BP curve can be obtained by differentiating (11.13):

( dr Xy n dY ) /3=0 —Kir —

265

The Foundation of Modern Macroeconomics

(i) X(Y, = 0

r*

Y

Figure 11.1. The degree of capital mobility and the balance of payment

X (Y, = 0

Figure 11.2. Monetary and fiscal policy with immobile capital and fixed exchange rates

Monetary and fiscal policy with immobile capital and fixed exchange rates

The IS curve is given by (11.9), the LM curve in (11.10)—(11.12), and the BP curve in (11.13) (with B = 0 and KI EF-- 0 imposed). Graphically the situation in the economy can be drawn as in Figure 11.2. The initial IS-LM-BP equilibrium is at point e0 where output is Yo and the interest rate is ro. Note that for points to the right of the BP curve output and imports are too high and the current account is in deficit (X < 0),

with the reverse ho output is below full conduct economic I Since the money!.

under fixed excha policy. An open rrh:.

bank leads to an ina in the money suppl shifts from LM(M0 ) the interest rate is lo (B = X < 0). Since 1 for foreign exchang( authority is come: satisfy the excess dc.1 reserves, i.e. ANFA`b (11.11), that the m, gradually shift to the

eo . Ultimately, the . . foreign exchange res(

bank's portfolio has I

Now consider

by means of fiscal p spending.2 Assume : cally produced goods Figure 11.2, the IS c rium is at point e". In account is in deficit 111 ) as the central ba: is at point el, at whit

In conclusion, neit of income in the aos

equilibrium if the cur of interest. This very of capital immobility

Monetary and fiscal fixed exchange rates

With perfect capital initial equilibrium is

2 The Treasury issues tit the money supply stays cc bond sale is spent again

266

'OB=0

B = 0

Y

Mr

r and the

LM (M2)

LM (M0)

LM (Mi )

It	is (Gi )

IS (GO)

•

Y

- h

r ed

11.12), and the BP curve in e situation in the economy librium is at point e0 where pints to the right of the BP ount is in deficit (X < 0),

Chapter 11: The Open Economy

with the reverse holding for points to the left of the BP curve. It is assumed that output is below full employment output YF and that the policy maker wishes to conduct economic policy aimed at restoring full employment.

Since the money supply is generally endogenous in the open economy operating under fixed exchange rates, we must be precise about what is meant by monetary policy. An open market operation in the form of a purchase of bonds by the central bank leads to an increase in domestic credit ADC > 0, and, by (11.11), to an increase in the money supply AMS = au ADC > 0. In terms of Figure 11.2, the LM curve shifts from LM(Mo) to LM(M1) in the short run. At point output is higher and the interest rate is lower than before the shock, but the current account is in deficit (B = X < 0). Since the country is spending more than it is earning, the demand for foreign exchange exceeds the supply of foreign exchange. Since the monetary authority is committed to maintaining a fixed exchange rate, however, it must satisfy the excess demand for foreign exchange by running down its international reserves, i.e. ANFACb < 0. In the absence of sterilization, this means, by equation (11.11), that the money stock starts to decrease again. This causes the LM curve to gradually shift to the left, and the economy moves along the IS curve back to point e0. Ultimately, the initial increase in domestic credit is exactly offset by the loss in foreign exchange reserves and only the composition (but not the size) of the central bank's portfolio has been changed as a result of the monetary policy.

Now consider what happens if the policy maker wishes to stimulate the economy by means of fiscal policy, consisting of a bond-financed increase in government spending. 2 Assume furthermore that government spending is entirely on domestically produced goods (a simplification that is relaxed below in section 2). In terms of Figure 11.2, the IS curve shifts from IS(Go ) to IS(Gi ) and the new short-run equilibrium is at point e". In view of the increase in output, imports are higher, the current account is in deficit (X < 0), and the money supply gradually declines (from Mo to M1 ) as the central bank foreign exchange reserves dwindle. The ultimate equilibrium is at point el, at which output is unchanged and the interest rate is higher.

In conclusion, neither monetary nor fiscal policy can (permanently) raise the level of income in the absence of capital mobility. The balance of payments is only in equilibrium if the current account is, but the latter does not itself depend on the rate of interest. This very strong conclusion is modified once the extreme assumption of capital immobility is relaxed.

Monetary and fiscal policy with perfect capital mobility under fixed exchange rates

With perfect capital mobility, the BP curve is horizontal. In terms of Figure 11.3, the initial equilibrium is at eo. Monetary policy, consisting of an increase in domestic

2 The Treasury issues new bonds to pay for the additional government spending. This ensures that the money supply stays constant as the level of domestic credit is unchanged. The money raised by the bond sale is spent again on the additional government goods.

267

The Foundation of Modern Macroeconomics

r

r*

Y

Figure 11.3. Monetary and fiscal policy with perfect capital mobility and fixed exchange rates

credit, shifts the LM curve from LM(M0) to LM(M1 ). At point e' the domestic interest rate is below the world interest rate and a massive capital outflow would occur, which worsens the capital account. Since output (and hence imports) is higher, the current account is also worse than at point e0. The money supply will decrease (instantaneously) as investors purchase foreign exchange in order to buy profitable foreign financial assets. Since the exchange rate is fixed, the monetary authority sells them the required foreign exchange, which means that its stock of net foreign assets decreases, i.e. ANFAth < 0. The adjustment occurs instantaneously, since all that happens is a portfolio reshuffling by investors. Hence, the economy stays at point e0. The shift in LM due to the increase in domestic credit is immediately reversed by the loss of foreign exchange reserves, or, in terms of (11.7), ANFAcb ± ADC= AH = 0. Monetary policy is totally ineffective even in the short run.

Fiscal policy, on the other hand, is very effective in this case. Consider again a bond-financed increase in government spending. In terms of Figure 11.3, the IS curve shifts to the right from IS(G0) to IS(G1). This puts upward pressure on the domestic interest rate (at point e") which causes massive net capital inflows. As investors from the ROW wish (in net terms) to buy domestic securities, the supply of foreign exchange outstrips the demand for foreign exchange. In order to maintain the fixed exchange rate, the central bank purchases the excess supply of foreign exchange and its stock of net foreign assets and hence the money supply increases (instantaneously), i.e. AMS = p,ANFAcb > 0. This causes the LM curve to shift from LM(M0) to LM(Mi). Only at point el are the domestic and foreign interest rates equated and the money supply stabilized. Since capital is perfectly mobile, the shift from e0 to el occurs instantaneously. Hence, fiscal policy is highly effective in a small open economy under perfect capital mobility.

Monetary and fiscal pa flexible exchange rates

Under flexible exchan ensure that the balan. rate is determined by 1 demand for and suppl)

B ANFAth = 0 4

where we have subs: exports. Suppose that t than imports. Since ex cause a demand for demand for foreign exl capital inflows, cons' they have to pay for th, exchange. In equilibriu then does demand equ

This has an imports authority has control rates. The reason is freely, does not need tc its stock of net forei Ets .. directly into changes

The equilibrium eN . imposed. By using (11 market and the (demai

M = L(r* , Y),

Y = A(r* , Y) + G

d

where we have also sub market equilibrium at constant (11.16) det. - exchange rate. In tei (11.17) represents do: - a high value for E (a N\ a positive relationship as the schedule YY obtained from (11.1,-

(c/E)y = 1 —A

dY y

268

P* = P = 1

fo)

1-M(A41)

IS (Gi)

IS (Go)

y

with perfect

point e' the domestic interAtal outflow would occur, d hence imports) is higher,

---. on ey supply will decrease r in order to buy profitable ed, the monetary authority that its stock of net forma occurs instantaneously,

• - estors. Hence, the econncrease in domestic credit reserves, or, in terms of lv ineffective even in the

is case. Consider again a ,rms of Figure 11.3, the IS

•c upward pressure on the e net capital inflows. As stic securities, the supply of e. In order to maintain e excess supply of foreign money supply increases e LM curve to shift from

and foreign interest rates - -erfectly mobile, the shift is highly effective in a

Chapter 11: The Open Economy

Monetary and fiscal policy with perfect capital mobility under cifxible exchange rates

Under flexible exchange rates variations in the value of the domestic currency (E) ensure that the balance of payments is always in equilibrium. Indeed, the exchange rate is determined by balance of payments equilibrium, since it implies that the demand for and supply of foreign exchange are equated:

B ANFAth = 0 <#. X( Y, E) + KI (r — r*) = 0, (11.15)

where we have substituted so that Q = E in the expression for net exports. Suppose that there is a current account deficit, so that exports are smaller than imports. Since exports give rise to a supply of foreign exchange and imports cause a demand for foreign exchange, this means that X < 0 represents an excess demand for foreign exchange. This excess demand for foreign exchange is met by capital inflows, consisting of investors from the ROW buying domestic bonds. Since they have to pay for these bonds, the capital inflow gives rise to a supply of foreign exchange. In equilibrium, therefore, E adjusts until X(Y , E) = —KI (r — r*) since only then does demand equal supply in the foreign exchange market.

This has an important consequence for economic policy, since the monetary authority has control over the domestic money supply under flexible exchange rates. The reason is that the central bank, by allowing the exchange rate to float freely, does not need to intervene in the foreign exchange market. This means that its stock of net foreign assets is fixed, so that changes in domestic credit translate directly into changes in the money supply.

The equilibrium exchange rate follows from the IS-LM equilibrium with r = r* imposed. By using (11.9)—(11.12) and imposing r = r*, equilibrium in the money market and the (demand side of the) goods market implies:

M = L(r* , Y),

Y A(r* , Y) + G + X (Y, E),

where we have also substituted P = 1 in (11.16). Equation (11.16) represents money market equilibrium at the given world interest rate r* . Since the money supply is constant (11.16) determines a unique level of output that is independent of the exchange rate. In terms of Figure 11.4, this curve is drawn as LL(Mo). Equation (11.17) represents domestic spending equilibrium at the world rate of interest. Since a high value for E (a weak domestic currency) stimulates net exports, (11.17) implies a positive relationship between output and the exchange rate that has been drawn as the schedule YY in Figure 11.4. Indeed, the slope of the YY schedule can be obtained from (11.17) as:

dE	1 - Ay -- Xy
dY YY	> 0.
	XQ

The Foundation of Modern Macroeconomics

(a)	r
				LM (M0)
				LM (Mi )
	r*
				IS(E1 )
				IS (E0)
		Yo	Y1	Y
(b)	E	LL (M0)	LL (Mi )
				YY
			ry
	E0		e

Figure 11.4. Monetary policy with perfect capital mobility and flexible exchange rates

Monetary policy is highly effective in this case. In terms of Figure 11.4, an increase in domestic credit shifts the LM curve in panel (a) from LM(M o ) to LM(M1 ) and the LL curve from LL(M0) to LL(M1 ). At point e' the domestic interest rate is below the world interest rate, and a massive capital outflow occurs. There is excess demand for foreign exchange which leads to an instantaneous depreciation of the domestic currency (from E0 to E1 in panel (b)). This stimulates net exports as domestic goods are now cheaper to foreigners and shifts the IS curve from IS(E0) to IS(E 1 ). The new equilibrium, which is attained instantaneously, is at point el where output is increased.

Fiscal policy, in the form of a bond-financed increase in government spending, turns out to be entirely ineffective (as was to be expected from the discussion surrounding the LL and YY curves). In terms of Figure 11.5, the fiscal impulse shifts the IS curve in panel (a) from IS(Go, E0) to IS(G1, E0), and the YY curve in panel (b) from

(b)

Figure and fit

YY(G0) to YY(G 1 ). Th: e' massive capital in.. response, the domes to a deterioration

E1 ), which coil attained instantaneo change rate has ap i

LAchange rates.

An immediate pol. t en economy oper, from foreign spendi - f Tided these sho,..1

%odd rate of interest

270

LM (Mo)

LM (Mi )

•

IS (E1 )

15(E0)

LL (Mi )

e, YY

capital

of Figure 11.4, an increase M(M0 ) to LM(M1 ) and the is interest rate is below the There is excess demand 7eciation of the domestic exports as domestic goods

IS(E0) to IS(E1). The it point el where output is

in government spending, d from the discussion sur- e fiscal impulse shifts the curve in panel (b) from

Chapter 11: The Open Economy

(b)

E

LL

yy (Go)

yy (G1)

E0

Y

Figure 11.5. Fiscal policy with perfect capital mobility and flexible exchange rates

YY(G0) to YY(G 1 ). This puts upward pressure on domestic interest rates and at point e' massive capital inflows occur leading to an excess supply for foreign exchange. In response, the domestic currency appreciates (E falls from E0 to E1 ), which leads to a deterioration of the current account and shifts IS back from IS(G1, E0) to IS(Gi , E1 ), which coincides with IS(Go, E0 ). In the new equilibrium, which is again attained instantaneously, output and the rate of interest are unchanged and the exchange rate has appreciated. Fiscal policy is completely ineffective under flexible

exchange rates.

An immediate policy consequence of this ineffectiveness result is that the small open economy operating under flexible exchange rates is, in a sense, insulated from foreign spending disturbances (such as shocks to the demand for its exports), provided these shocks are uncoordinated and consequently have no effect on the world rate of interest. For example, if a spending bust occurs in Germany leading

271

(b) E

The Foundation of Modern Macroeconomics

to a decrease in the demand for exports from the Netherlands, the Dutch exchange rate will depreciate and no output effects will occur under flexible exchange rates. Matters are different, of course, if a global shock hits the economy. If all countries, except the Netherlands, pursue expansionary aggregate demand policies, the world interest rate will rise. This will affect the Dutch economy even if it is operating under flexible exchange rates. In terms of Figure 11.6, the rise in r* shifts the YY

(a)r

LM

ei

ri

ro

Yo

Yi

LL (ro)

YY (ro)

curve to the left and the due to the capital out: the small open econom,

to the issue of shock tral 1

Imperfect capital mobi

If financial capital is imp vious extreme cases. The and points to the left : ments surplus (deficit). 1 where the BP curve has fiscal and monetary pol means, we present the in Table 11.1. The re, differentiate the IS, LM,

Ly L, 1 —Ay — Xy —.a

(XY / Mr)	1
	4

Of course, equation (11. on the left-hand side s.. however, by specifying t

r

ro

ri

Figure 11.6. Foreign interest rate shocks with perfect capital	Figure 11.7.
mobility and flexible exchange rates	flexible exctki

272

ands, the Dutch exchange 'der flexible exchange rates. ke economy. If all countries, demand policies, the world omv even if it is operating the rise in r* shifts the YY

LM

IS (Ei )

Y

Chapter 11: The Open Economy

curve to the left and the LL curve to the right. The domestic currency depreciates, le to the capital outflows, and output increases. A global shock is transmitted to the small open economy through its effect on the world rate of interest. We return

to the issue of shock transmission below.

'llperfect capital mobility

If financial capital is imperfectly mobile, we have a weighted average of the two pre-. vious extreme cases. The balance of payments curve is upward sloping (see (11.14)) and points to the left (right) of the BP curve are consistent with a balance of payments surplus (deficit). The IS, LM, and BP curves have been drawn in Figure 11.7, where the BP curve has been drawn flatter than the LM curve. Instead of discussing fiscal and monetary policy under fixed and flexible exchange rates by graphical means, we present the different comparative static effects in mathematical form in Table 11.1. The results in Table 11.1 are obtained as follows. First we totally differentiate the IS, LM, and BP curves. After some manipulations we obtain:

	Ly Lr 0 —1	dY	0
		dr
	1— Ay — Xy —A r —XQ 0		=[dGl.
		dE
	(Xy /KG) 1 (XQ/Kr) 0		dr*
		dM
	[

Of course, equation (11.19) cannot be used to solve for all four variables appearing on the left-hand side since we only have three equations. This "problem" is solved however, by specifying the exchange rate regime. Under flexible exchange rates the

	Yo	Y1	Y
'{ Pct capital	Figure 11.7. Monetary policy with imperfect capital mobility and
	flexible exchange rates

273

The Foundation of Modern Macroeconomics

Table 11.1. Capital mobility and comparative static effects

dG

dM

dr*

Flexible exchange rates

LA >0

dY

LA/K4

4(1 - Ar/K1r) > 0

> 0

'Al

ii

dr

L yXQ /Kl,. > 0

XQ(1 - AO/Kir < 0

0 <

Ly4

ILS1

-

iAi

-

— < 1

IAI —

dE LrXy /KIr - L y

< 0

1 - A y - Xy

+ArXy /KIr

>

-Ar Ly - Lr (1 - Ay - Xy)

>0

lAi

>

iAl

iAi

Fixed exchange rates

dY

I F I

>0

-Ar/mr) > o

Ar

0

IF'

in <

Xy/KIr >

(1 -AoxaKir < 0

0 <

1 -Ay - Xy

<1

Irl

- 0

Irl

Irl

LrXy/KIry - iAt

Ar L y 1-r (1

dM

Irl

0

Irl > 0

in- AY Xy) < 0

Notes: 101 XQ Ry (1 — Ar/ Klr) — Lr(1 AY)/K1,1 > 0

in

-

A y - Xy +ArXy /KI, > 0

money supply is exogenous (and the column for dM is moved to the right-hand side of (11.19)) and (11.19) determines dY, dr, and dE, as a function of the exogenous variables dM, dG, and dr*. Under fixed exchange rates, on the other hand, the exchange rate is exogenous (and the column for dE is moved to the right-hand side of (11.19)) and (11.19) determines dY, dr, and dM, as a function of the exogenous variables dE, dG, and dr*.

In order to demonstrate the link between the mathematical results in Table 11.1 and the graphical representation in Figure 11.7, consider the case of monetary policy under flexible exchange rates. The increase in domestic credit shifts the LM curve from LM(Mo) to LM(M1 ). At point e', output and imports are too high and net capital inflows too low, so that there exists a balance of payments deficit (B < 0), which manifests itself as an excess demand for foreign exchange. The domestic currency depreciates (E rises), the IS curve shifts from IS(E0) to IS(E 1 ), and the BP curve shifts from BP(E0) to BP(E 1 ). Both the current account and the capital account recover somewhat due to the depreciation and the slight recovery of the domestic interest rate (that occurs in moving from e' to e1). The new equilibrium is at el. Although it is impossible to deduce by graphical means, the results in Table 11.1 demonstrate that the ultimate effect on output is positive.

Of course, since the results of Table 11.1 are derived for any value of Klr , the polar cases of immobile and perfectly mobile capital can be obtained as special cases from the table by setting KIr = 0 and K/, oo, respectively. The students are advised to verify that this is indeed the case.

11.1.4 Aggregates

Up to this point we L

(P = P* = 1). Whilst .. short run), it is nevertl model of the small of (1979), Armington (19 importance of supply-I in section 2 on the tra, in a two-country mod capital mobility and :..

The Armington approa

Now that we wish to r more precise about th with price P, and a NI,. of the foreign good in each other (otherwise that the real exchange Real household con% • the usual macro-relatiu

C = C(Y), I = /(r

with 0 < Cy < 1 and I, We now need to coy. the households know I real terms, the next is (and the same holds fo trick that was devised I fact "constructed" out produced goods (labelli substitutes, we cannot the same as a Dutch at particularly simple way

C = Cl-a

df

with 0 < a < 1 denoti. used in consumption.

In the decision about sumption level C (that possible. Since the (dot

274